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Question
Areas of two similar triangles are 225 sq.cm. 81 sq.cm. If a side of the smaller triangle is 12 cm, then Find corresponding side of the bigger triangle.
Solution
Let areas of two similar triangles be A1 and A2 & their corresponding sides be S1 and S2
A1 = 225 sq.cm, A2 = 81 sq.cm
S2 = 12 cm, S1 = ?
`"A"_1/"A"_2="S"_1^2/"S"_2^2` ...[Theorem of areas of similar triangle]
`225/81="S"_1^2/(12)^2`
Taking square root on both side
`sqrt(225/81)=sqrt("S"_1/12)`
`15/9="S"_1/12`
`15/9xx12="S"_1`
∴ S1 = 20 cm
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